College Algebra in Context : With Applications for the Managerial, Life, and Social Sciences

Why Rent from Knetbooks?

Because Knetbooks knows college students. Our rental program is designed to save you time and money. Whether you need a textbook for a semester, quarter or even a summer session, we have an option for you. Simply select a rental period, enter your information and your book will be on its way!

Learn the Skills. Apply the Concepts. This second EDITION of College Algebra in Context continues to be application driven, and uses real-data problems to motivate student interest in the skills and concepts of algebra. The focus on real-world applications is designed to correspond to problems that students may encounter when they move on to future math classes or when they enter the work force. This EDITION contains improved content and a greater focus on motivating students to succeed in the course through its emphasis on applications.

Preface

xiii

List of Supplements

xvii

To the Student

xix

Functions, Graphs, and Models; Linear Functions

1

(138)

Algebra Toolbox

2

(8)

Sets

2

(1)

The Real Numbers

3

(1)

Inequalities and Intervals on the Number Line

4

(1)

Absolute Value

5

(1)

Algebraic Expressions

5

(1)

Removing Parentheses

6

(1)

Solving Equations

6

(2)

The Coordinate System

8

(1)

Subscripts

8

(2)

Functions and Models

10

(17)

Function Definitions

10

(2)

Tests for Functions

12

(2)

Functional Notation

14

(2)

Mathematical Models

16

(1)

Domains and Ranges

17

(10)

Graphs of Functions

27

(14)

Graphs of Functions

27

(1)

Graphing with Technology

28

(4)

Aligning Data

32

(1)

Determining Viewing Windows

32

(2)

Graphing Data Points

34

(7)

Linear Functions

41

(14)

Linear Functions

41

(1)

Intercepts

42

(3)

Slope of a Line

45

(2)

Slope and y-Intercept of a Line

47

(2)

Constant Rate of Change

49

(1)

Parallel and Perpendicular Lines

50

(5)

Equations of Lines

55

(15)

Writing Equations of Lines

55

(5)

Average Rate of Change

60

(2)

Approximately Linear Data

62

(8)

Algebraic and Graphical Solutions of Linear Equations

70

(12)

Algebraic Solution of Linear Equations

71

(2)

Solutions, Zeros, and x-lntercepts

73

(1)

Graphical Solution of Linear Equations

74

(3)

Formulas; Solving an Equation for a Specified Linear Variable

77

(5)

Fitting Lines to Data Points; Modeling Linear Functions

82

(20)

Fitting Lines to Data Points

82

(3)

Linear Regression

85

(3)

Modeling Discrete Data with Linear Functions

88

(4)

Applying Models

92

(1)

Goodness of Fit

92

(10)

Systems of Linear Equations in Two Variables

102

(12)

Graphical Solution of Systems

102

(3)

Solution by Substitution

105

(2)

Solution by Elimination

107

(1)

Modeling Systems of Linear Equations

108

(2)

Inconsistent and Dependent Systems

110

(4)

Solutions of Linear Inequalities

114

(25)

Algebraic Solution of Linear Inequalities

114

(3)

Graphical Solution of Linear Inequalities

117

(2)

x-lntercept Method

119

(1)

Double Inequalities

120

(6)

Summary

126

(1)

Key Concepts and Formulas

126

(5)

Skills Check

131

(1)

Review

132

(5)

Group Activities/Extended Applications

137

(2)

Quadratic and Other Nonlinear Functions

139

(136)

Algebra Toolbox

140

(14)

Properties of Exponents

140

(1)

Roots and Radicals

141

(1)

Radicals and Rational Exponents

142

(1)

Polynomials

143

(1)

Multiplication of Polynomials

144

(2)

Factoring

146

(3)

Solving Literal Equations

149

(1)

Imaginary and Complex Numbers

149

(1)

Operations with Complex Numbers

150

(4)

Quadratic Functions; Parabolas

154

(11)

Parabolas

154

(5)

Quadratic Functions in the Form f(x) = a(x - h)2 + k

159

(1)

Intercepts

160

(5)

Solving Quadratic Equations

165

(16)

Factoring Methods

165

(2)

Graphical Methods

167

(1)

Combining Graphs and Factoring

168

(2)

Graphical and Numerical Methods

170

(1)

The Square Root Method

170

(1)

Completing the Square

171

(1)

The Quadratic Formula

172

(2)

The Discriminant

174

(1)

Aids for Solving Quadratic Equations

175

(1)

Equations with Compiex Solutions

175

(6)

A Library of Functions

181

(12)

Power Functions

181

(4)

Reciprocal Function

185

(2)

Piecewise-Defined Functions

187

(2)

Absolute Value Function

189

(4)

Transformations of Graphs and Symmetry

193

(15)

Shifts of Graphs of Functions

193

(3)

Stretching and Compressing Graphs

196

(1)

Reflections of Graphs

197

(3)

Symmetry; Even and Odd Functions

200

(8)

Quadratic and Power Models

208

(17)

Modeling with Quadratic Functions

208

(1)

Comparison of Linear and Quadratic Models

209

(3)

Modeling with Power Functions

212

(2)

Comparison of Power and Quadratic Models

214

(11)

Combining Functions; Composite Functions

225

(12)

Operations with Functions

225

(1)

Revenue, Cost, and Profit

226

(3)

CompSsition of Functions

229

(8)

Inverse Functions

237

(12)

Inverse Functions

237

(6)

Inverse Functions on Limited Domains

243

(6)

Additional Equations and Inequalities

249

(26)

Radical Equations; Equations Involving Rational Powers

249

(2)

Equations Containing Rational Powers

251

(1)

Solving Absolute Value Equations

252

(1)

Inequalities Involving Absolute Values

253

(1)

Solution of Quadratic Inequalities

254

(4)

Power Inequalities

258

(3)

Summary

261

(1)

Key Concepts and Formulas

262

(4)

Skills Check

266

(1)

Review

267

(6)

Group Activities/Extended Applications

273

(2)

Exponential and Logarithmic Functions

275

(94)

Algebra Toolbox

276

(5)

Zero and Negative Exponents

276

(2)

Scientific Notation

278

(1)

Simple Interest

279

(2)

Exponential Functions

281

(10)

Exponential Functions

281

(1)

Transformations of Graphs of Exponential Functions

282

(1)

Exponential Growth

283

(2)

Exponential Decay

285

(1)

The Number e

286

(5)

Logarithmic Functions

291

(12)

Logarithmic Functions

291

(4)

Common Logarithms

295

(2)

Natural Logarithms

297

(2)

Solution of Logarithmic Equations

299

(4)

Exponential and Logarithmic Equations; Properties of Logarithms

303

(14)

Solving Exponential Equations Using Logarithmic Forms

303

(2)

Logarithmic Properties

305

(3)

Change of Base

308

(2)

Solving Exponential Equations Using Logarithmic Properties

310

(2)

Solution of Logarithmic Equations

312

(1)

Exponential thequalities

313

(4)

Exponential and Logarithmic Models

317

(15)

Modeling with Exponential Functions

317

(3)

Constant Percent Change in Exponential Models

320

(2)

Exponential Models

322

(1)

Comparison of Models

323

(1)

Logarithmic Models

324

(3)

Exponents, Logarithms, and Linear Regression

327

(5)

Exponential Functions and Investing

332

(9)

Compound Interest

332

(2)

Continuous Compounding and the Number e

334

(3)

Present Value of an Investment

337

(1)

Investment Models

338

(3)

Annuities; Loan Repayment

341

(8)

Future Value of an Annuity

341

(2)

Present Value of an Annuity

343

(1)

Loan Repayment

344

(5)

Logistic and Gompertz Functions

349

(20)

Logistic Functions

349

(5)

Gompertz Functions

354

(5)

Summary

359

(1)

Key Concepts and Formulas

359

(3)

Skills Check

362

(1)

Review

363

(4)

Group Activities/Extended Applications

367

(2)

Higher-Degree Polynomial and Rational Functions

369

(76)

Algebra Toolbox

370

(7)

Polynomiais

370

(1)

Factoring Higher-Degree Polynomials

370

(1)

Rational Expressions

371

(1)

Multiplying and Dividing Rational Expressions

372

(1)

Adding and Subtracting Rational Expressions

373

(1)

Division of Polynomiais

374

(3)

Higher-Degree Polynomial Functions

377

(10)

Cubic Functions

378

(3)

Quartic Functions

381

(6)

Modeling Cubic and Quartic Functions

387

(13)

Modeling with Cubic Functions

387

(3)

Modeling with Quartic Functions

390

(1)

Model Comparisons

391

(1)

Third and Fourth Differences

392

(8)

Solution of Polynomial Equations

400

(10)

Solving Polynomial Equations by Factoring

400

(3)

Solution Using Factoring by Grouping

403

(1)

The Root Method

403

(2)

Estimating Solutions with Technology

405

(5)

Polynomial Equations Continued; Fundamental Theorem of Algebra

410

(10)

Division of Polynomials; Synthetic Division

410

(2)

Using Synthetic Division to Solve Cubic Equations

412

(1)

Graphs and Solutions

412

(2)

Rational Solutions Test

414

(2)

Fundamental Theorem of Algebra

416

(4)

Rational Functions and Rational Equations

420

(11)

Graphs of Rational Functions

420

(5)

Analytical and Graphical Solution of Rational Equations

425

(6)

Polynomial and Rational Inequalities

431

(14)

Polynomial Inequalities

431

(2)

Rational Inequalities

433

(4)

Summary

437

(1)

Key Concepts and Formutas

437

(3)

Skills Check

440

(1)

Review

441

(2)

Group Activities/Extended Applications

443

(2)

Systems of Equations and Matrices

445

(74)

Algebra Toolbox

446

(4)

Proportion

446

(1)

Proportional Triples

447

(1)

Linear Equations in Three Variables

447

(3)

Systems of Linear Equations in Three Variables

450

(11)

Systems in Three Variables

450

(1)

Left-to-Right Elimination

451

(2)

Modeling Systems of Equations

453

(1)

Nonunique Solutions

454

(7)

Matrix Solution of Systems of Linear Equations

461

(14)

Matrix Representation of Systems of Equations

461

(1)

Echelon Forms of Matrices; Solving Systems with Matrices

462

(2)

Gauss-Jordan Elimination

464

(1)

Solution with Technology

465

(1)

Nonunique Solution

466

(1)

Dependent Systems

467

(2)

Inconsistent Systems

469

(6)

Matrix Operations

475

(15)

Addition and Subtraction of Matrices

475

(4)

Multiplication of a Matrix by a Number

479

(1)

Matrix Multiplication

480

(3)

Multiplication with Technology

483

(7)

Inverse Matrices; Matrix Equations

490

(14)

Inverse Matrices

490

(2)

Inverses and Technology

492

(1)

Encoding and Decoding Messages

493

(3)

Matrix Equations

496

(2)

Matrix Equations and Technology

498

(6)

Systems of Nonlinear Equations

504

(15)

Algebraic Solution of Nonlinear Systems

504

(3)

Graphical Solution of Nonlinear Systems

507

(4)

Summary

511

(1)

Key Concepts and Formulas

511

(2)

Skills Check

513

(1)

Review

514

(3)

Group Activities/Extended Applications

517

(2)

Special Topics: Systems of Inequalities and Linear Programming; Sequences and Series; Preparing for Calculus